Things that glow under UV light are taking in UV, and giving off visible light. The brighness of the glow is directly related to the strength of the UV light, but for the kind of event you are talking about, the glow could be pretty dim. Obviously the ambient light level will make a bid difference as to how things will show up, but I would guess you should be prepared for some very low light levels of both the ambient and the UV glow. Do you happen to have one of the newer cameras that do pretty well in low light? For one project I shot, where the light level was pretty low and changed quite a bit, I shot with a fast lens wide open on manual with a fixed shutter speed that I could hand hold, and then used Auto ISO with no limit on how high the ISO would go. I had a lot of keepers doing that. It is of course difficult to auto focus in low light, so be prepared to do manual focus by eye, or even focus by setting the distance scale on the lens.

You should for sure try things out with the AV company, even if it is just a quick test in a small room. You should probably be prepared with a flash that you can bounce off the ceiling and set the power very low, so that you can suplement the available light a bit, but only at a low fill level that does not overpower the UV glow on the guests. And remember, because of the unusual situation, you have a built in excuse to have limited depth of field, motion effects, poor color balance, and lots of noise showing in the images. Shooting from a tripod and having lots of planned motion effects is another approach that could come out well.

Google it. There are a lot posts about yhis topic. A true uv filter on your flash might work

I'd look into getting or converting a small speed light into a uv source. Low light + dark room + people made up is a tough gig .
I had to shoot something like this back in the film days but we had time to test and it was a still life situation.
I really don't know how digital sensors react. It may be as simple as a ultra hi iso and some work in PS or LR.

I've shot in a UV lit environment before, it was a kids Halloween party. Yes, the UV effect does show up. However, it's a very low light level. My exposures were around 1/250 at f/1.2 and ISO 16,000. If you aren't shooting with super fast glass and a modern camera with excellent high ISO performance, you'll have a tough time.

Focusing is a challenge in light that low. You might consider using the focus assist on a shoe mount flash to help acquire focus in the dark conditions.

Thanks for the help. I've been searching Google of course, but experience from those who've actually done it is invaluable.

Fortunately I'm blessed with 5D3's and 24-70 / 70-200 F2.8 lenses as my usual suspects, but with 35 / 50 and 85 L series lenses in case so low light can be dealt with. (Although shutter speed needs to capture fast moving kids and focus on fast moving kids can be fun if it's F1.2...

Not sure how I'd get a speedlight to work as a UV source but I'll certainly have a look...

I'm suspecting ISO 6400 as a minimum and a lower keeper rate than I'd prefer may be the solution, with noise reduction in post.

I've shot kids' events at ISO 6400 with 1/50 sec 200mm F2.8 regularly, as some of my clients like to have low light with moving LED coloured lighting and heavy smoke machines on the go - so I'm used to difficult conditions. This one will prove to be no exception!